The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a mixing matrix from S4 family symmetry and generalized CP symmetry HCP. Supposing that S4 ⋊ HCP is broken down to Z2ST2SU×HCPν\documentclass[12pt]{minimal}
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\begin{document}$$ {Z}_2^{S{T}^2SU}\times {H}_{\mathrm{CP}}^{\nu } $$\end{document} in the neutrino sector and Z4TST2U⋊HCPl\documentclass[12pt]{minimal}
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\begin{document}$$ {Z}_4^{TS{T}^2U}\rtimes {H}_{\mathrm{CP}}^l $$\end{document} in the charged lepton sector, one column of the PMNS matrix would be of the form 1/2,1/2,1/2T\documentclass[12pt]{minimal}
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\begin{document}$$ {\left(1/2,1/\sqrt{2},1/2\right)}^T $$\end{document} up to permutations, both Dirac CP phase and Majorana CP phases are trivial to accommodate the observed lepton mixing angles. The phenomenological implications of the remnant symmetry K4TST2,T2U×HCPν\documentclass[12pt]{minimal}
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\begin{document}$$ {K}_4^{\left(TS{T}^2,{T}^2U\right)}\times {H}_{\mathrm{CP}}^{\nu } $$\end{document} in the neutrino sector and Z2SU × HCPl in the charged lepton sector are studied. One row of PMNS matrix is determined to be 1/2,1/2,−i/2\documentclass[12pt]{minimal}
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\begin{document}$$ \left(1/2,1/2,-i/\sqrt{2}\right) $$\end{document}, and all the three leptonic CP phases can only be trivial to fit the measured values of the mixing angles. Two models based on S4 family symmetry and generalized CP are constructed to implement these model independent predictions enforced by remnant symmetry. The correct mass hierarchy among the charged leptons is achieved. The vacuum alignment and higher order corrections are discussed.
